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Common Belief with the Logic of Individual Belief
Author(s) -
Bonanno Giacomo,
Nehring Klaus
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/(sici)1521-3870(200001)46:1<49::aid-malq49>3.0.co;2-r
Subject(s) - axiom , mathematics , belief structure , belief revision , operator (biology) , subjective logic , epistemology , computer science , artificial intelligence , mathematical economics , probabilistic logic , philosophy , biochemistry , chemistry , statistics , geometry , repressor , transcription factor , gene
The logic of common belief does not always reflect that of individual beliefs. In particular, even when the individual belief operators satisfy the KD45 logic, the common belief operator may fail to satisfy axiom 5. That is, it can happen that neither is A commonly believed nor is it common belief that A is not commonly believed. We identify the intersubjective restrictions on individual beliefs that are incorporated in axiom 5 for common belief.